Results 61 to 70 of about 516,382 (294)
On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials
Mathematics, 2020 The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers. This generalization provides new integral and differential representations in addition to new mathematical results that are ...
Mohra Zayed +3 more
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Congruences concerning Legendre polynomials II [PDF]
Journal of Number Theory, 2013 Suppose that p is an odd prime and d is a positive integer. Let x and y be integers given by p = x2+dy2 or 4p = x2+dy2. In this paper we determine x( mod p) for many values of d. For example, [Formula: see text] where x is chosen so that x ≡ 1 ( mod 3). We also pose some conjectures on supercongruences modulo p2 concerning binary quadratic forms.
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This study examines the combined impact of different thermal conductivity and viscosity on unsteady non‐Newtonian Casson fluid flow of incompressible, electrical conductivity in a porous vertical channel with convective cooling walls, uniform magnetic field, and constant pressure gradient.
A. S. Adeyemo +2 more
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Supersymmetry, shape invariance and the hypergeometric equation
, 2014 It has been shown earlier that the solubility of the Legendre and the associated Legendre equations can be understood as a consequence of an underlying supersymmetry and shape invariance. We have extended this result to the hypergeometric equation. Since
Das, Ashok K., Kalauni, Pushpa
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Oikos, EarlyView.Biodiversity dynamics in heterogeneous landscapes is the result of a complex interplay between movement processes of organisms within and between habitat patches, and niche filtering processes due to spatially varying environmental conditions. Disentangling the relative influences of these different processes on community assembly and dynamics is a ...
Gwenaelle Auger +6 more
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A Property of Legendre Polynomials [PDF]
Proceedings of the National Academy of Sciences, 1970 Remark I: The Legendre polynomials are the spherical functions for the symmetric space SO(3)/SO(2). A property analogous to that stated in the above theorem holds for other symmetric spaces. In this fashion we get also new properties for Gegenbauer polynomials, Bessel, and Legendre functions.
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Legendre Polynomials: a Simple Methodology
Journal of Physics: Conference Series, 2019 Legendre polynomials are obtained through well-known linear algebra methods based on Sturm-Liouville theory. A matrix corresponding to the Legendre differential operator is found and its eigenvalues are obtained. The elements of the eigenvectors obtained
V. Aboites
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Addressing ecological challenges from a quantum computing perspective
Methods in Ecology and Evolution, EarlyView.Abstract With increased access to data and the advent of computers, the use of statistical tools and numerical simulations is becoming commonplace for ecologists. These approaches help improve our understanding of ecological phenomena and their underlying mechanisms in increasingly complex environments.
Maxime Clenet +2 more
wiley +1 more source
Animal Conservation, EarlyView.Identifying the most effective criterion to assess the conservation status of vulnerable species in threatened tropical regions is crucial to evaluate recovery plans. We investigated the influence of environmental heterogeneity on the extent of occurrence (EOO), area of occupied habitat (AOH), and density variation of two Amazonian riparian frog ...
Rafael F. Jorge +3 more
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DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER WITH ORTHOGONAL POLYNOMIAL SOLUTIONS
Pesquimat, 2014 In this paper we developed conditions for orthogonality of polynomial Solutions of the fourth order differential equations with polynomial coefficients.
Santiago César Rojas Romero
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